After witnessing one of the most abject Liverpool displays in the long history of this derby, John W Henry and his colleagues might now wonder if they, rather than their predecessors, are the victims of an epic swindle.

They could be forgiven for thinking they’ve been had and for starting to worry that they paid too much for Liverpool — even at the price Tom Hicks and George Gillett have claimed is way below market value.

This performance against a vastly superior Everton side would suggest you don’t get much for £300million these days, so inept were Liverpool’s players in trying to ease the pressure on Roy Hodgson.

That pressure must now be considerable, whatever statements have been made in the last 72 hours.

‘We’re here to win,’ said Henry in delivering his mission statement on Friday but right now these Liverpool players do not even appear capable of winning a relegation battle.

It was, as the Everton supporters declared in joyous unison at the sound of the final whistle, ‘easy’ for a side that continues to impress under the expert guidance of David Moyes.

Magic Mikel: Arteta extends Liverpool's misery

Goals from Tim Cahill and Mikel Arteta secured their second win in as many games to propel the club away from the danger zone and up the Barclays Premier League table. There was little in response from Liverpool.

No urgency, no fluency. Nothing, the occasional Jamie Carragher outburst aside, that even resembled what you might term defiance. That Hodgson thought his team played well will only weaken his position.

He thought this was their finest performance of the season; that his team played well; that in no way, particularly in the second half, were they either lacking in confidence or inferior to their hosts. On Friday he also said that, had that defeat to Blackpool at Anfield been scored on a boxing-style points system, his team would have emerged triumphant.

But then he would also have us believe that the £20m he spent on Raul Meireles, Paul Konchesky and Christian Poulsen amounts to good business. Liverpool’s new owners say they are not going to walk into Anfield ‘like a bull in china shop’ and start making immediate changes.

But before they commit money to the next transfer window in January, when some major surgery on the squad will be required, they might have serious misgivings about letting Hodgson be the man who spends it.

He thought only Fernando Torres was lacking confidence, when so many players appeared to be struggling yesterday. Players such as Konchesky, Meireles, Joe Cole, Maxi Rodriguez and Lucas looked like they would rather be anywhere but here at Goodison.

As a drama it was absorbing. The sight of Liverpool players hiding; the sight of Hodgson watching helplessly from the technical area, seemingly cemented to the ground where he stood and unable to inspire any kind of fightback from his troops; and then the sight, at the front of the directors’ box, of Henry deep in conversation with a colleague during the half-time interval.

One can only imagine what was being discussed. Perhaps Henry was expressing his regret in not sticking to his guns and saving his first taste of English football for a game at Anfield. But even someone as new to this game as the Americans would have seen that something needs to be done — and fast — to revive this stuttering side.

Perhaps Kenny Dalglish, sitting behind the new owners yesterday, has one or two ideas. Hodgson still appears to think he can turn the situation round and it would be wrong to dismiss a manager of his considerable experience.

But even for Hodgson this must be unique pressure and the evidence at Goodison suggested he is starting to struggle. Everton had endured a difficult start to the season, too, but they responded to their manager when Moyes decided to ‘get back to basics’.

‘It wasn’t just because we went mountain climbing,’ he said.

‘It’s been a lot of hard work. The players haven’t had much time off lately.’

They were working from the start of this encounter, not least for each other. Where Liverpool were disjointed, Everton were determined and organised. Where Liverpool lacked spirit, Everton possessed a collective will to win.

They dominated the opening half, scoring the goal their skill and industry deserved in the 34th minute when the hugely promising Seamus Coleman surged past both Lucas and Konchesky before delivering a perfect ball for Cahill.

It still demanded a terrific right-foot finish from the Australian international, who became Everton’s highest post-war goalscorer in league Merseyside derbies. But Coleman’s run exposed the ineptitude of Liverpool’s defending.

Less could have been done about the goal that followed from Arteta five minutes after the break. It was a quite brilliant strike and one that was all the more impressive because Moyes revealed the Spaniard had been a doubt due to a hamstring injury suffered in training on Saturday.

Only then did Liverpool even begin to react. Only then did Liverpool’s players even seem aware that this might not be the ideal way to respond to the arrival of new owners. Not that their response amounted to much.

After taking only six points from eight games, they now sit second from bottom in the Premier League. And while many would no doubt disagree with Alan Hansen when he suggested this was Liverpool’s biggest game in 30 years, it is probably their lowest ebb.

It is certainly hard to recall a Liverpool team worse than this one and hard to imagine that Hodgson will be given long to prove otherwise.